APTS module: Computer Intensive Statistics

Please see the full Module Specifications for background information relating to all of the APTS modules, including how to interpret the information below.

Aims: This module will introduce various computationally-intensive methods and their background theory, including material on simulation-based approaches such as Markov-chain Monte Carlo (MCMC) and the bootstrap, and on strategies for handling large datasets. The different methods will be illustrated by applications.

Learning outcomes: After taking this module, students will have a working appreciation of MCMC, the bootstrap and other simulation-based methods and of their limitations, and have some experience of implementing them for simple examples.

Prerequisites: Preparation for this module should include a review of:

familiarity with basic types of convergence of random variables: in probability, almost sure and in distribution (as for example covered in Shiryaev, 1996; or Rosenthal, 2006);

relevant basic material on statistical modelling (for which the earlier APTS module 'Statistical Modelling' would be advantageous; see also Davison, 2003);

basic Markov chains (as for the 'Applied Stochastic Processes' module; relevant further reading can be found in Shiryaev, 1996);

basic knowledge of programming in a high-level language such as R (R will be used for case studies and exercises). An introduction to R can be found here.